Problem 10

$\large \frac{1}{\sqrt[4]{a^2+b^2}}+\frac{1}{\sqrt[4]{b^2+c^2}}+\frac{1}{\sqrt[4]{c^2+a^2}}$

Given that $a,b,c$ are non-negative and at the same time two of three of the triple of numbers are non-zero and $a+b+c=2$ . Find the minimum value of the expression above.

Give your answer to two decimal places.

This problem is in this Set .